完全分配格代数中秩一子代数的弱稠密性和套代数的一个特征

李鹏同;鲁世杰

数学学报 ›› 2002, Vol. 45 ›› Issue (1) : 59-64.

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PDF(430 KB)
数学学报 ›› 2002, Vol. 45 ›› Issue (1) : 59-64. DOI: 10.12386/A2002sxxb0008
论文

完全分配格代数中秩一子代数的弱稠密性和套代数的一个特征

    李鹏同;鲁世杰
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The Weak Density of the Rank One Subalgebra in Completely Distributive Subspace Lattice Algebras and a Characterization of Nest Algebras

    Peng Tong LI(1),Shi Jie LU(2)
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摘要

如果 A是 Hilbert 空间上的完全分配格代数,  那么A中秩一算子生成的子代数在 A中弱稠密, 当且仅当,A在迹尖算子空间中的一次和二次预零化子的弱闭包是自反的;如果A是套代数,那么LatA是极大套,当且仅当,A的包含A-的每个弱闭子空间是自反的,其中 

Abstract

If A is a completely distributive subspace lattice algebra on a Hilbert space, then the rank one subalgebra of A is weak dense in A if and only if, the weak closures of the first and the second preannihilators of A in the space of all trace class operators are reflexive. If A is a nest algebra, then Lat, A , the nest of all invariant subspaces of A, is maximal if and only if, all of the weak closed subspaces of A containing A-are reflexive.

关键词

完全分配格 / 极大套 / 弱拓扑 / 稠密 / 零化子 / 自反

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李鹏同;鲁世杰. 完全分配格代数中秩一子代数的弱稠密性和套代数的一个特征. 数学学报, 2002, 45(1): 59-64 https://doi.org/10.12386/A2002sxxb0008
Peng Tong LI(1),Shi Jie LU(2). The Weak Density of the Rank One Subalgebra in Completely Distributive Subspace Lattice Algebras and a Characterization of Nest Algebras. Acta Mathematica Sinica, Chinese Series, 2002, 45(1): 59-64 https://doi.org/10.12386/A2002sxxb0008
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